{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6044c434-1b4c-4ace-a81e-07f12c55658a",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "ae794c6a-fc19-44f5-b720-14528502b4e0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2798790551489746\n"
     ]
    }
   ],
   "source": [
    "a = [6, 1, 2, 0, 12, 1, 0, 1, 2, 5, 2, 1, 2, 1, 2, 5, 1, 1, 2, 2, 11, 4, 1, 0, 4, 4, 5, 7, 0, 3, 3, 2, 0, 3, 8, 4, 1, 5, 2, 6, 0, 1, 3, 5, 2, 1, 0, 2, 3, 0, 0, 3, 2, 2, 1, 3, 4, 15, 0, 5, 2, 1, 4, 2, 0, 0, 2, 2, 9, 1, 5, 5, 5, 1, 1, 12, 1, 7, 1, 0, 8, 3, 0, 3, 8, 3, 4, 9, 30, 6, 10, 9, 14, 31, 4, 34, 32, 7, 9, 1, 34, 5, 7, 14, 0, 9, 5, 0, 32, 6, 8, 27, 22, 24, 4, 17, 5, 16, 3, 25, 34, 8, 51, 23, 8, 62, 4, 8, 15, 4, 11, 55, 14, 12, 5, 5, 10, 6, 10, 1, 23, 9, 19, 7, 10, 5, 3, 9, 1, 7, 3, 0, 6, 0, 36, 7, 55, 43, 17, 24, 1, 3, 17, 6, 2, 16, 21, 20, 3, 14, 67, 1, 3, 19, 53, 61, 6, 34, 29, 12, 13, 9, 29, 17, 43, 5, 43, 0, 40, 55, 3, 12, 43, 5, 15, 1, 6, 55, 1, 10, 0, 3, 7, 6, 9, 68, 0, 66, 8, 22, 25, 49, 60, 2, 32, 65, 69, 18, 30, 55, 33, 11, 4, 42, 36, 15, 12, 17, 23, 56, 11, 2, 17, 11, 15, 37, 7, 41, 9, 13, 23, 45, 19, 0, 6, 1, 5, 10, 41, 7, 9, 1, 7, 10, 13, 0, 0, 8, 4, 5, 1, 9, 5, 5, 57, 5, 35, 12, 15, 1, 10, 26, 2, 2, 0, 20, 35, 50, 4, 5, 19, 31, 0, 8, 14, 60, 7, 42, 10, 77, 36, 32, 23, 2, 48, 2, 46, 13, 14, 12, 30, 70, 2, 4, 24, 1, 78, 45, 2, 22, 19, 12, 5, 26, 7, 3, 21, 31, 52, 15, 28, 84, 5, 9, 4, 53, 6, 1, 30, 55, 2, 11, 11, 63, 19, 8, 23, 4, 4, 56, 12, 21, 27, 46, 36, 41, 35, 6, 1, 68, 69, 2, 16, 18, 10, 0, 23, 11, 6, 18, 20, 36, 5, 76, 39, 17, 69, 4, 66, 7, 70, 10, 39, 40, 6, 12, 60, 65, 4, 63, 10, 35, 9, 27, 66, 58, 61, 42, 49, 73, 42, 30, 42, 66, 49, 11, 6, 3, 50, 36, 32, 2, 49, 13, 3, 35, 74, 83, 3, 18, 68, 8, 64, 43, 56, 32, 65, 38, 19, 60, 62, 69, 72, 74, 66, 19, 40, 60, 38, 89, 54, 62, 29, 68, 72, 21, 14, 14, 83, 44, 22, 33, 30, 56, 62, 29, 21, 79, 17, 16, 83, 40, 24, 17, 38, 72, 21, 19, 18, 32, 66, 26, 85, 16, 30, 16, 73, 21, 29, 23, 42, 54, 71, 44, 15, 26, 85, 80, 31, 76, 71, 44, 21, 15, 65, 79, 55, 55, 83, 48, 14, 26, 72, 31, 30, 68, 70, 61, 53, 44, 86, 53, 8, 74, 76, 25, 23, 39, 33, 17, 66, 43, 9, 73, 37, 43, 53, 41, 27, 46, 51, 65, 30, 40, 70, 5, 20, 66, 11, 26, 25, 62, 85, 49, 69, 54, 75, 77, 45, 43, 8, 7, 64, 51, 44, 39, 24, 75, 69, 55, 68, 55, 49, 69, 25, 67, 40, 25, 68, 51, 34, 46, 57, 54, 64, 42, 69, 71, 43, 58, 35, 67, 55, 56, 56, 61, 30, 13, 63, 59, 39, 38, 31, 40, 64, 57, 65, 58, 61, 55, 58, 67, 63, 35, 56, 69, 10, 64, 60, 49, 53, 14, 50, 66, 16, 56, 6, 33, 10, 27, 39, 51, 33, 44, 49, 56, 28, 68, 16, 45, 64, 32, 72, 72, 44, 66, 48, 47, 74, 56, 41, 61, 74, 57, 41, 28, 67, 61, 45, 55, 60, 48, 56, 33, 26, 52, 50, 19, 11, 55, 25, 48, 57, 20, 47, 66, 42, 49, 85, 36, 60, 33, 77, 58, 68, 67, 29, 56, 56, 19, 48, 68, 57, 72, 66, 36, 43, 52, 64, 56, 25, 60, 49, 69, 62, 47, 67, 70, 57, 74, 46, 66, 57, 80, 83, 56, 56, 77, 70, 54, 24, 60, 76, 69, 85, 43, 13, 67, 69, 29, 54, 36, 71, 36, 72, 12, 74, 71, 28, 76, 59, 65, 66, 60, 73, 52, 48, 34, 55, 29, 67, 78, 68, 27, 67, 46, 58, 70, 67, 67, 80, 71, 68, 70, 73, 64, 53, 79, 59, 30, 62, 74, 69, 79, 51, 37, 62, 57, 68, 65, 30, 75, 63, 48, 64, 81, 62, 73, 60, 16, 41, 68, 71, 60, 30, 69, 55, 70, 45, 73, 56, 12, 61, 58, 61, 39, 76, 70, 46, 69, 54, 74, 61, 51, 64, 77, 51, 37, 64, 68, 43, 50, 84, 61, 66, 64, 69, 77, 69, 21, 76, 28, 68, 15, 82, 61, 71, 44, 74, 48, 51, 6, 23, 67, 45, 47, 56, 71, 69, 47, 78, 65, 68, 69, 86, 55, 36, 77, 80, 35, 17, 48, 80, 63, 66, 29, 66, 71, 68, 73, 71, 54, 79, 52, 83, 62, 58, 77, 82, 46, 69, 68, 70, 91, 59, 77, 65, 72, 53, 63, 74, 21, 58, 20, 44, 68, 53, 54, 36, 60, 84, 53, 82, 60, 32, 23, 54, 77, 60, 60, 52, 37, 62, 72, 33, 80, 44, 51, 41, 66, 62, 79, 52, 36, 38, 40, 77, 70, 62, 43, 78, 45, 77, 31, 69, 38, 33, 80, 74, 75, 75, 31, 48, 64, 18, 78, 77, 73, 35, 76, 82, 79, 34, 83, 71, 52, 55, 80, 64, 80, 88, 84, 78, 85, 36, 84, 83, 57, 62, 83, 87, 21, 85, 76, 83, 61, 85, 87, 88, 78, 84, 83, 90, 80, 82, 39, 93, 34, 36, 80, 66, 58, 84, 69, 77, 79, 76, 77, 74, 82, 29, 73, 72, 84, 77, 33, 25, 73, 60, 79, 71, 74, 91, 72, 77, 45, 74, 77, 78, 73, 87, 88, 50, 80, 46, 68, 31, 25, 95, 78, 80, 92, 75, 86, 89, 85, 80, 37, 78, 69, 55, 78, 83, 81, 43, 32, 56, 84, 78, 78, 78, 78, 50, 76, 54, 76, 73, 81, 16, 83, 78, 75, 67, 42, 92, 91, 60, 37, 79, 89, 32, 28, 29, 62, 33, 74, 76, 27, 74, 83, 90, 88, 39, 40, 71, 78, 82, 52, 47, 82, 76, 79, 81, 61, 89, 70, 38, 53, 42, 43, 47, 82, 85, 89, 46, 45, 7, 26, 80, 48, 53, 90, 83, 85, 91, 82, 87, 78, 29, 74, 36, 77, 68, 76, 77, 88, 51, 82, 87, 75, 83, 47, 34, 85, 13, 86, 29, 67, 86, 31, 75, 82, 95, 23, 87, 90, 47, 39, 91, 80, 92, 24, 90, 44, 93, 37, 89, 84, 34, 90, 43, 92, 20, 34, 24, 59, 86, 90, 36, 90, 86, 69, 33, 34, 88, 83, 54, 66, 89, 35, 41, 57, 20, 91, 38, 86, 41, 42, 97, 44, 62, 91, 91, 90, 87, 92, 51, 87, 95, 90, 93, 37, 56, 84, 31, 91, 37, 94, 23, 92, 52, 40, 15, 30, 30, 43, 52, 79, 88, 31, 22, 56, 41, 28, 20, 90, 48, 35, 36, 58, 63, 45, 52, 33, 59, 33, 53, 75, 12, 64, 77, 83, 93, 75, 88, 88, 71, 76, 95, 50, 83, 47, 44, 37, 89, 94, 29, 91, 86, 48, 90, 66, 89, 71, 46, 89, 86, 68, 85, 88, 26, 45, 68, 43, 58, 47, 1, 45, 50, 94, 90, 32, 39, 33, 48, 46, 86, 94, 34, 66, 87, 59, 38, 92, 24, 43, 41, 89, 92, 34, 92, 39, 91, 91, 54, 92, 53, 91, 27, 92, 89, 73, 89, 94, 96, 92, 74, 16, 86, 85, 82, 32, 92, 89, 44, 92, 23, 57, 75, 39, 52, 92, 87, 84, 7, 94, 92, 35, 32, 17, 25, 98, 88, 35, 36, 36, 25, 91, 36, 95, 24, 91, 37, 40, 93, 94, 27, 38, 19, 91, 89, 91, 91, 40, 74, 90, 97, 87, 56, 91, 26, 25, 85, 92, 41, 92, 33, 44, 48, 62, 50, 91, 44, 46, 37, 31, 37, 90, 39, 98, 94, 36, 95, 98, 20, 96, 93, 51, 36, 46, 56, 87, 91, 94, 95, 49, 42, 33, 33, 49, 48, 45, 96, 44, 54, 44, 30, 94, 46, 90, 94, 35, 34, 44, 86, 46, 79, 27, 58, 43, 41, 43, 84, 32, 34, 48, 41, 56, 95, 96, 88, 90, 91, 83, 91, 48, 22, 89, 92, 94, 90, 93, 37, 95, 57, 43, 96, 32, 66, 58, 41, 88, 96, 87, 36, 51, 46, 41, 86, 54, 89, 43, 51, 87, 43, 34, 92, 45, 34, 49, 40, 44, 87, 49, 94, 34, 94, 47, 56, 95, 97, 47, 52, 94, 95, 48, 89, 87, 39, 93, 88, 86, 93, 89, 96, 90, 30, 94, 88, 40, 87, 38, 86, 94, 37, 41, 36, 96, 27, 41, 88, 28, 45, 89, 40, 35, 35, 92, 97, 91, 43, 92, 88, 93, 55, 56, 91, 49, 82, 90, 55, 88, 97, 36, 55, 91, 97, 51, 37, 95, 88, 64, 92, 44, 96, 31, 91, 92, 67, 45, 40, 25, 19, 96, 36, 92, 90, 60, 54, 96, 96, 88, 48, 93, 98, 95, 91, 88, 95, 99, 94, 58, 40, 59, 39, 89, 91, 31, 98, 29, 99, 93, 97, 45, 44, 95, 49, 91, 95, 91, 54, 95, 94, 91, 47, 95, 42, 48, 28, 47, 27, 47, 91, 39, 33, 45, 31, 97, 21, 97, 43, 51, 45, 91, 92, 39, 92, 51, 83, 90, 93, 39, 93, 44, 93, 91, 44, 41, 48, 47, 94, 93, 90, 47, 46, 95, 45, 88, 54, 48, 40, 93, 41, 91, 57, 49, 96, 66, 39, 92, 96, 92, 60, 44, 96, 95, 93, 50, 92, 49, 62, 95, 43, 90, 60, 90, 83, 98, 49, 54, 50, 93, 53, 91, 93, 93, 87, 91, 94, 39, 90, 97, 91, 93, 90, 47, 45, 98, 92, 87, 90, 44, 41, 45, 52, 93, 97, 96, 49, 93, 99, 93, 88, 54, 90, 53, 94, 93, 54, 29, 33, 50, 30, 97, 99, 94, 98, 40, 55, 92, 86, 90, 94, 58, 58, 86, 47, 44, 85, 85, 93, 85, 96, 31, 40, 60, 95, 97, 49, 41, 56, 44, 45, 49, 89, 55, 59, 46, 58, 29, 93, 45, 49, 44, 30, 44, 37, 51, 40, 54, 58, 52, 56, 55, 40, 49, 51, 60, 95, 41, 35, 47, 40, 42, 47, 49, 54, 54, 44, 93, 44, 38, 37, 51, 44, 37, 57, 94, 45, 46, 51, 50, 45, 45, 50, 50, 45, 37, 48, 51, 47, 48, 47, 95, 58, 59, 57, 92, 48, 66, 54, 30, 47, 43, 50, 94, 42, 46, 94, 90, 53, 48, 51, 56, 45, 48, 37, 41, 32, 52, 55, 53, 53, 90, 95, 91, 56, 56, 50, 45, 53, 51, 50, 44, 44, 31, 28, 40, 49, 53, 44, 42, 46, 52, 49, 63, 55, 49, 59, 92, 94, 41, 64, 53, 63, 52, 52, 51, 64, 69, 95, 96, 92, 43, 98, 94, 83, 97, 91, 45, 94, 88, 53, 96, 50, 41, 39, 40, 50, 40, 47, 44, 40, 98, 36, 91, 44, 92, 41, 89, 46, 89, 94, 39, 88, 90, 41, 96, 44, 97, 98, 90, 90, 43, 90, 42, 97, 91, 92, 42, 90, 90, 43, 97, 90, 42, 86, 87, 39, 96, 44, 44, 39]\n",
    "b = [2, 2, 2, 2, 1, 2, 2, 2, 2, 3, 2, 2, 2, 3, 2, 4, 3, 2, 2, 2, 4, 2, 2, 3, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 3, 2, 2, 1, 2, 4, 2, 2, 2, 2, 3, 3, 7, 2, 2, 2, 3, 5, 3, 2, 2, 3, 2, 2, 2, 4, 5, 3, 2, 2, 3, 7, 3, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 2, 5, 3, 3, 4, 2, 2, 2, 2, 2, 2, 3, 1, 1, 2, 2, 2, 2, 1, 1, 3, 5, 2, 2, 2, 3, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 1, 2, 2, 3, 1, 2, 1, 2, 1, 2, 1, 2, 1, 3, 2, 4, 3, 1, 1, 3, 2, 2, 2, 2, 1, 2, 2, 1, 1, 7, 2, 2, 1, 2, 2, 2, 2, 2, 4, 2, 3, 1, 2, 1, 1, 2, 2, 2, 1, 3, 2, 1, 2, 1, 1, 2, 6, 1, 3, 2, 2, 2, 1, 6, 2, 1, 2, 2, 2, 1, 4, 1, 2, 2, 2, 3, 1, 2, 2, 2, 2, 3, 2, 2, 1, 2, 5, 2, 2, 2, 2, 2, 1, 3, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 1, 2, 1, 5, 2, 1, 2, 1, 2, 1, 1, 3, 2, 2, 2, 1, 1, 2, 1, 2, 2, 4, 2, 2, 2, 3, 2, 4, 4, 2, 2, 2, 2, 3, 4, 2, 4, 2, 2, 2, 2, 5, 4, 4, 2, 1, 3, 6, 2, 1, 2, 3, 2, 2, 2, 4, 1, 2, 2, 2, 4, 2, 1, 3, 2, 2, 1, 2, 1, 3, 1, 1, 1, 2, 5, 1, 2, 3, 2, 5, 3, 2, 3, 2, 5, 2, 2, 1, 3, 2, 1, 3, 1, 2, 1, 2, 2, 3, 1, 2, 1, 2, 1, 4, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 1, 4, 4, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 4, 2, 1, 1, 2, 3, 4, 1, 2, 3, 2, 5, 1, 3, 2, 5, 1, 4, 2, 1, 6, 1, 6, 1, 2, 1, 2, 3, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2, 1, 3, 1, 1, 1, 3, 2, 2, 2, 7, 3, 2, 1, 1, 1, 2, 3, 1, 2, 3, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 3, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 3, 1, 1, 1, 4, 3, 2, 2, 1, 2, 1, 1, 1, 2, 3, 2, 2, 1, 1, 1, 2, 4, 1, 1, 1, 3, 3, 1, 1, 1, 3, 3, 1, 2, 1, 1, 2, 2, 2, 2, 1, 4, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 3, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 6, 2, 2, 2, 3, 2, 1, 4, 1, 1, 2, 1, 5, 2, 1, 5, 3, 1, 1, 1, 1, 4, 1, 2, 3, 2, 2, 2, 1, 1, 1, 2, 1, 4, 1, 1, 1, 1, 2, 1, 4, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 3, 1, 2, 1, 1, 2, 2, 1, 2, 1, 3, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 2, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 4, 1, 2, 1, 3, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 1]\n",
    "c = [22, 15, 18, 16, 25, 22, 17, 19, 20, 27, 25, 15, 24, 25, 17, 20, 16, 21, 21, 25, 26, 19, 20, 19, 27, 21, 27, 18, 17, 16, 16, 22, 19, 17, 22, 26, 18, 23, 19, 21, 15, 24, 21, 17, 14, 16, 21, 17, 17, 16, 15, 16, 18, 20, 22, 16, 24, 22, 17, 20, 15, 23, 27, 16, 11, 24, 14, 19, 22, 18, 25, 22, 23, 16, 14, 25, 21, 14, 12, 14, 17, 23, 10, 13, 20, 15, 19, 14, 32, 18, 17, 12, 15, 27, 23, 29, 24, 24, 18, 11, 27, 13, 15, 23, 16, 26, 18, 16, 26, 24, 18, 27, 19, 26, 19, 23, 22, 26, 25, 24, 31, 25, 24, 26, 22, 20, 21, 12, 12, 20, 15, 23, 26, 24, 18, 31, 20, 12, 22, 14, 23, 23, 18, 18, 25, 12, 14, 23, 14, 24, 8, 13, 11, 16, 21, 12, 22, 27, 25, 24, 18, 15, 19, 19, 16, 35, 26, 27, 15, 27, 17, 16, 12, 27, 22, 22, 20, 25, 29, 23, 15, 19, 27, 28, 30, 22, 26, 18, 19, 25, 22, 19, 20, 25, 19, 16, 22, 18, 16, 22, 16, 15, 20, 21, 26, 19, 7, 23, 17, 28, 22, 22, 24, 13, 18, 18, 15, 28, 21, 24, 21, 18, 15, 23, 27, 18, 23, 19, 17, 20, 23, 13, 27, 29, 21, 27, 25, 24, 16, 31, 24, 31, 16, 11, 20, 18, 22, 22, 23, 19, 18, 11, 18, 11, 25, 15, 12, 20, 13, 16, 3, 20, 13, 9, 22, 16, 20, 21, 26, 17, 12, 28, 18, 25, 9, 23, 23, 21, 18, 10, 29, 33, 11, 11, 22, 14, 14, 22, 20, 20, 22, 22, 15, 16, 18, 16, 30, 18, 18, 17, 25, 20, 12, 10, 13, 16, 15, 29, 19, 12, 17, 15, 9, 19, 18, 14, 17, 19, 20, 19, 18, 13, 14, 18, 11, 27, 13, 18, 26, 25, 15, 15, 11, 16, 23, 5, 12, 11, 13, 19, 15, 22, 27, 15, 18, 19, 25, 10, 14, 17, 19, 12, 19, 23, 15, 14, 17, 13, 15, 17, 14, 22, 10, 12, 17, 16, 9, 10, 15, 17, 12, 15, 23, 26, 9, 14, 15, 10, 14, 19, 8, 19, 22, 17, 14, 16, 11, 27, 28, 15, 9, 13, 12, 15, 21, 9, 9, 4, 17, 18, 12, 9, 10, 17, 13, 19, 13, 10, 11, 13, 9, 11, 13, 21, 12, 14, 5, 24, 15, 18, 23, 17, 8, 7, 13, 10, 19, 11, 8, 4, 19, 12, 16, 12, 16, 10, 16, 7, 14, 19, 10, 18, 12, 14, 16, 15, 11, 18, 15, 9, 9, 17, 16, 12, 14, 17, 10, 15, 5, 15, 12, 12, 7, 3, 14, 2, 9, 6, 13, 14, 12, 16, 11, 13, 9, 15, 5, 4, 10, 5, 11, 13, 15, 9, 16, 10, 10, 9, 4, 18, 10, 14, 16, 14, 12, 5, 13, 17, 19, 12, 8, 20, 13, 13, 11, 16, 13, 11, 17, 15, 12, 12, 15, 9, 10, 15, 11, 14, 11, 19, 10, 7, 18, 11, 16, 10, 9, 12, 14, 11, 13, 13, 13, 6, 8, 18, 12, 7, 12, 17, 12, 11, 8, 13, 10, 4, 10, 8, 10, 17, 11, 10, 8, 5, 9, 22, 7, 11, 16, 13, 15, 17, 16, 12, 12, 9, 12, 11, 15, 15, 10, 15, 15, 6, 9, 16, 10, 10, 13, 10, 23, 11, 6, 16, 15, 16, 9, 13, 9, 20, 9, 14, 11, 12, 13, 8, 11, 6, 15, 9, 7, 9, 17, 13, 7, 7, 12, 12, 11, 16, 12, 18, 6, 9, 15, 7, 15, 12, 7, 9, 12, 13, 10, 11, 3, 15, 18, 9, 4, 10, 7, 13, 9, 11, 8, 11, 10, 10, 12, 13, 10, 12, 13, 13, 11, 14, 21, 8, 4, 8, 8, 4, 11, 7, 16, 4, 6, 13, 12, 6, 6, 14, 7, 12, 8, 7, 8, 11, 9, 10, 13, 9, 14, 7, 14, 8, 12, 8, 12, 7, 13, 5, 12, 11, 8, 10, 8, 9, 10, 10, 7, 15, 8, 7, 7, 10, 7, 13, 9, 7, 8, 9, 9, 15, 7, 11, 11, 10, 6, 9, 9, 7, 5, 7, 11, 12, 6, 6, 10, 6, 5, 8, 7, 9, 4, 10, 8, 2, 5, 11, 5, 7, 7, 1, 8, 7, 9, 5, 5, 6, 6, 3, 5, 9, 12, 9, 12, 2, 14, 4, 5, 4, 4, 4, 12, 9, 6, 8, 3, 7, 10, 5, 9, 13, 7, 7, 4, 11, 6, 8, 6, 8, 6, 10, 3, 9, 9, 5, 10, 4, 9, 6, 15, 7, 7, 12, 11, 5, 10, 6, 10, 9, 0, 4, 9, 6, 6, 10, 9, 8, 6, 9, 6, 10, 12, 8, 8, 6, 7, 7, 5, 8, 5, 13, 6, 4, 4, 5, 5, 8, 5, 5, 2, 5, 4, 10, 9, 2, 6, 12, 4, 3, 4, 7, 5, 12, 6, 5, 5, 4, 8, 3, 6, 6, 3, 8, 5, 6, 6, 4, 4, 5, 6, 14, 3, 6, 11, 3, 5, 7, 10, 7, 3, 4, 6, 5, 1, 9, 7, 5, 9, 7, 5, 3, 5, 1, 6, 6, 7, 2, 3, 9, 4, 6, 6, 4, 7, 3, 5, 9, 3, 7, 2, 7, 7, 8, 8, 8, 2, 7, 5, 1, 8, 8, 9, 1, 2, 6, 13, 6, 2, 7, 4, 6, 12, 4, 5, 5, 5, 5, 2, 2, 3, 5, 2, 2, 3, 7, 7, 3, 5, 5, 4, 8, 2, 4, 8, 5, 5, 4, 4, 4, 3, 4, 8, 7, 3, 8, 5, 3, 3, 8, 8, 5, 9, 8, 2, 4, 1, 2, 6, 4, 3, 6, 6, 4, 2, 5, 9, 5, 8, 6, 2, 6, 6, 3, 5, 3, 4, 5, 4, 5, 2, 1, 2, 4, 3, 6, 6, 4, 4, 8, 5, 7, 6, 7, 2, 3, 5, 2, 3, 3, 8, 4, 4, 4, 6, 4, 3, 6, 7, 1, 5, 7, 0, 5, 8, 5, 4, 6, 5, 3, 5, 1, 5, 0, 9, 8, 3, 3, 1, 3, 4, 5, 5, 4, 6, 5, 4, 3, 4, 9, 5, 5, 2, 1, 3, 5, 6, 3, 4, 6, 3, 6, 2, 10, 6, 5, 6, 6, 4, 5, 2, 5, 6, 5, 3, 4, 4, 5, 4, 3, 2, 10, 3, 1, 4, 9, 9, 7, 6, 5, 4, 6, 5, 5, 3, 7, 5, 3, 8, 3, 5, 1, 3, 2, 6, 6, 2, 8, 6, 2, 5, 5, 3, 6, 7, 7, 3, 3, 8, 7, 10, 4, 5, 3, 6, 4, 7, 4, 5, 3, 1, 6, 4, 5, 3, 5, 4, 8, 5, 9, 4, 5, 4, 5, 5, 3, 1, 2, 4, 3, 5, 6, 3, 2, 8, 3, 5, 4, 2, 2, 7, 5, 5, 4, 6, 6, 3, 1, 4, 1, 5, 3, 6, 5, 4, 0, 1, 3, 4, 5, 2, 7, 3, 3, 6, 7, 4, 4, 5, 2, 6, 6, 1, 4, 4, 2, 3, 3, 5, 6, 8, 6, 4, 6, 1, 6, 4, 4, 3, 6, 5, 2, 6, 3, 4, 5, 7, 4, 4, 4, 3, 5, 5, 5, 4, 3, 2, 3, 5, 4, 1, 2, 1, 5, 4, 4, 2, 5, 2, 2, 1, 5, 5, 1, 5, 3, 6, 3, 6, 2, 4, 1, 3, 3, 3, 4, 5, 6, 3, 4, 2, 1, 3, 4, 7, 1, 2, 1, 2, 2, 3, 3, 2, 3, 3, 3, 5, 1, 4, 3, 2, 4, 3, 7, 4, 7, 5, 2, 4, 2, 6, 6, 5, 4, 2, 6, 2, 5, 8, 2, 2, 3, 1, 3, 2, 1, 6, 5, 3, 5, 5, 2, 5, 3, 2, 4, 6, 4, 0, 5, 2, 8, 7, 2, 4, 6, 1, 3, 3, 0, 3, 0, 5, 4, 7, 3, 4, 2, 1, 4, 3, 4, 3, 3, 2, 3, 0, 5, 4, 6, 5, 6, 7, 6, 1, 5, 1, 3, 6, 7, 6, 2, 1, 4, 3, 1, 3, 1, 1, 3, 1, 2, 3, 1, 3, 6, 2, 1, 3, 3, 2, 0, 2, 3, 4, 3, 6, 4, 1, 3, 6, 2, 1, 2, 5, 6, 0, 3, 0, 3, 0, 5, 2, 4, 2, 2, 4, 6, 2, 0, 0, 3, 6, 3, 7, 2, 3, 3, 5, 1, 7, 6, 1, 0, 4, 1, 3, 1, 3, 5, 5, 7, 0, 2, 5, 2, 3, 3, 4, 4, 2, 2, 3, 2, 1, 3, 1, 3, 0, 2, 1, 5, 3, 0, 4, 0, 5, 4, 4, 3, 2, 5, 1, 8, 5, 3, 1, 1, 3, 1, 5, 4, 3, 1, 3, 4, 2, 3, 0, 2, 2, 2, 2, 2, 4, 6, 3, 4, 5, 6, 5, 2, 0, 1, 4, 2, 4, 0, 5, 0, 4, 2, 2, 2, 2, 2, 2, 3, 5, 1, 3, 3, 3, 2, 3, 4, 1, 3, 5, 3, 4, 0, 0, 4, 3, 1, 7, 4, 2, 7, 2, 2, 1, 2, 2, 3, 6, 1, 3, 1, 5, 0, 0, 2, 2, 2, 2, 3, 2, 5, 3, 2, 2, 7, 5, 1, 0, 3, 1, 6, 4, 3, 0, 3, 3, 6, 2, 0, 2, 1, 4, 4, 2, 7, 2, 2, 1, 0, 0, 4, 1, 3, 3, 2, 2, 6, 2, 6, 2, 2, 3, 4, 5, 2, 2, 1, 8, 1, 7, 5, 5, 1, 3, 4, 4, 2, 4, 1, 2, 1, 4, 6, 5, 0, 4, 4, 9, 6, 3, 2, 3, 5, 5, 2, 1, 1, 1, 1, 3, 5, 7, 5, 3, 3, 3, 5, 1, 0, 2, 3, 2, 5, 4, 2, 2, 1, 1, 1, 2, 5, 5, 2, 1, 2, 5, 0, 6, 2, 2, 2, 1, 6, 3, 4, 9, 1, 2, 5, 2, 4, 1, 2, 3, 5, 9, 5, 3, 2, 6, 1, 5, 3, 6, 3, 2, 0, 4, 8, 6, 2, 3, 0, 1, 5, 2, 0, 1, 5, 0, 3, 6, 1, 4, 1, 2, 3, 2, 2, 5, 1, 2, 1, 0, 4, 1, 1, 2, 4, 3, 3, 2, 2, 1, 4, 2, 4, 6, 4, 2, 5, 1, 3, 1, 1, 3, 1, 0, 1, 1, 3, 2, 1, 7, 2, 0, 3, 1, 2, 4, 3, 1, 2, 0, 1, 4, 0, 1, 1, 0, 3, 1, 5, 5, 3, 2, 2, 2, 1, 7, 4, 3, 2, 1, 2, 1, 3, 3, 5, 2, 1, 4, 2, 0, 0, 2, 5, 1, 3, 1, 1, 5, 3, 2, 1, 1, 2, 3, 2, 0, 0, 3, 3, 1, 1, 3, 6, 2, 4, 2, 2, 2, 5, 6, 3, 6, 0, 2, 7, 3, 1, 2, 2, 1, 2, 0, 2, 4, 1, 0, 1, 4, 5, 2, 5, 0, 1, 4, 1, 5, 1, 3, 2, 1, 0, 0, 1, 6, 2, 2, 1, 0, 1, 2, 2, 2, 1, 2, 4, 4, 1, 3, 3, 1, 1, 1, 2, 1, 2, 3, 3, 6, 2, 0, 2, 10, 1, 3, 1, 3, 7, 1, 2, 1, 2, 1, 4, 3, 1, 5, 6, 4, 1, 4, 4, 3, 3, 2, 4, 2, 6, 4, 0, 7, 2, 0, 2, 1, 1, 0, 5, 5, 2, 5, 2, 1, 4, 3, 2, 6, 4, 0, 1, 4, 6, 8, 4, 2, 2, 0, 3, 2]\n",
    "d = [70, 82, 78, 82, 62, 75, 81, 78, 76, 65, 71, 82, 72, 71, 79, 71, 80, 76, 75, 71, 59, 75, 77, 78, 67, 73, 66, 74, 80, 79, 79, 74, 79, 78, 67, 68, 79, 71, 77, 69, 83, 73, 74, 76, 81, 80, 72, 79, 78, 82, 82, 76, 77, 76, 75, 78, 70, 61, 81, 71, 78, 73, 67, 80, 86, 69, 81, 78, 67, 79, 68, 71, 70, 81, 82, 60, 75, 77, 82, 83, 72, 70, 88, 82, 70, 80, 75, 75, 35, 75, 72, 77, 69, 40, 71, 36, 43, 66, 68, 86, 37, 80, 75, 61, 82, 63, 75, 82, 38, 68, 72, 44, 57, 49, 75, 58, 70, 57, 70, 50, 33, 66, 23, 50, 68, 17, 72, 78, 69, 73, 73, 21, 57, 62, 75, 62, 68, 81, 66, 83, 53, 67, 56, 73, 63, 82, 81, 66, 83, 67, 87, 83, 81, 81, 42, 79, 22, 29, 56, 50, 79, 81, 61, 73, 81, 47, 52, 52, 80, 53, 15, 80, 83, 52, 23, 16, 68, 39, 41, 63, 70, 70, 43, 51, 26, 71, 29, 80, 38, 19, 73, 67, 35, 68, 63, 81, 70, 26, 81, 63, 82, 80, 71, 71, 63, 12, 90, 10, 74, 48, 52, 27, 15, 83, 48, 15, 15, 52, 47, 20, 44, 70, 76, 33, 36, 65, 64, 62, 59, 23, 63, 83, 54, 58, 63, 35, 66, 34, 73, 54, 49, 22, 63, 87, 71, 79, 69, 64, 34, 72, 71, 86, 72, 75, 60, 81, 86, 70, 81, 77, 91, 67, 78, 84, 20, 76, 39, 65, 58, 80, 75, 44, 78, 71, 87, 56, 40, 27, 76, 81, 50, 35, 86, 79, 62, 25, 77, 35, 67, 2, 41, 45, 60, 77, 33, 80, 21, 67, 63, 68, 43, 7, 84, 81, 61, 81, 6, 23, 77, 65, 61, 72, 84, 54, 73, 81, 59, 49, 26, 65, 52, 2, 77, 71, 83, 19, 79, 79, 41, 18, 81, 72, 75, 20, 54, 83, 63, 83, 81, 23, 71, 56, 45, 38, 44, 39, 38, 80, 83, 14, 11, 84, 62, 55, 74, 84, 57, 74, 74, 64, 63, 40, 80, 11, 40, 65, 21, 80, 18, 70, 17, 73, 37, 32, 82, 73, 23, 24, 80, 17, 80, 44, 67, 54, 19, 24, 27, 28, 22, 11, 48, 54, 44, 17, 28, 73, 82, 91, 32, 45, 55, 87, 38, 69, 82, 43, 12, 6, 84, 68, 22, 79, 22, 34, 31, 52, 29, 37, 65, 21, 14, 13, 19, 17, 20, 69, 38, 28, 52, 6, 26, 24, 54, 19, 10, 67, 68, 76, 2, 36, 67, 45, 55, 28, 20, 55, 66, 2, 67, 74, 6, 40, 58, 69, 47, 10, 68, 64, 73, 52, 21, 61, 5, 78, 55, 81, 17, 70, 55, 62, 44, 29, 17, 41, 74, 57, 8, 15, 55, 18, 17, 42, 62, 74, 18, 10, 34, 35, 12, 33, 75, 58, 11, 54, 55, 25, 16, 20, 26, 43, 5, 26, 77, 12, 12, 57, 62, 48, 48, 67, 20, 44, 74, 16, 50, 41, 35, 43, 60, 34, 38, 26, 51, 48, 13, 82, 69, 21, 73, 61, 61, 24, 1, 44, 22, 27, 12, 14, 42, 34, 78, 80, 26, 33, 44, 56, 62, 16, 20, 26, 20, 30, 41, 25, 61, 8, 52, 63, 15, 35, 47, 36, 25, 31, 22, 47, 17, 17, 41, 26, 53, 17, 26, 37, 34, 22, 59, 75, 23, 27, 37, 49, 62, 43, 20, 26, 25, 27, 29, 24, 32, 18, 25, 52, 29, 21, 77, 29, 24, 41, 39, 76, 31, 20, 76, 36, 80, 54, 77, 56, 47, 30, 60, 46, 34, 35, 55, 19, 76, 45, 23, 54, 17, 16, 52, 18, 33, 43, 19, 33, 51, 24, 16, 31, 50, 59, 22, 28, 42, 31, 29, 39, 28, 53, 61, 33, 28, 71, 83, 36, 65, 47, 29, 71, 35, 29, 51, 37, 2, 57, 33, 51, 15, 29, 23, 25, 62, 32, 34, 69, 38, 21, 28, 20, 19, 55, 43, 38, 23, 35, 60, 34, 38, 18, 29, 42, 23, 20, 31, 15, 45, 17, 33, 12, 9, 33, 36, 9, 20, 36, 67, 30, 14, 14, 7, 45, 75, 21, 24, 61, 36, 56, 23, 53, 16, 74, 19, 20, 60, 17, 34, 26, 26, 30, 22, 37, 43, 62, 39, 58, 27, 14, 24, 71, 24, 46, 32, 21, 27, 26, 12, 25, 26, 20, 13, 26, 34, 18, 26, 64, 32, 21, 26, 16, 36, 53, 31, 34, 28, 27, 58, 19, 27, 38, 28, 11, 33, 15, 33, 75, 52, 23, 22, 29, 65, 21, 35, 24, 44, 22, 34, 80, 23, 34, 31, 48, 12, 24, 43, 24, 35, 16, 38, 44, 25, 15, 41, 52, 25, 23, 50, 40, 9, 28, 21, 27, 22, 16, 22, 71, 18, 62, 26, 70, 10, 34, 24, 50, 20, 43, 43, 88, 73, 27, 50, 42, 34, 26, 23, 40, 17, 31, 27, 22, 8, 32, 56, 17, 14, 59, 73, 47, 13, 30, 30, 61, 28, 22, 25, 22, 24, 40, 14, 33, 12, 30, 30, 18, 11, 46, 20, 24, 26, 4, 34, 17, 33, 18, 39, 31, 16, 70, 36, 75, 50, 29, 40, 39, 55, 37, 12, 37, 13, 33, 61, 71, 37, 18, 34, 30, 44, 54, 35, 20, 59, 11, 47, 40, 55, 26, 32, 19, 39, 55, 51, 58, 19, 23, 24, 50, 19, 47, 18, 61, 18, 56, 60, 14, 20, 19, 22, 66, 47, 30, 78, 19, 19, 19, 57, 20, 12, 15, 61, 8, 26, 43, 36, 14, 30, 15, 7, 11, 18, 10, 55, 8, 13, 34, 31, 13, 9, 70, 6, 18, 7, 30, 12, 8, 10, 19, 9, 12, 6, 13, 11, 55, 4, 59, 54, 14, 25, 35, 13, 24, 16, 17, 18, 19, 21, 12, 65, 21, 25, 14, 20, 62, 71, 20, 33, 16, 24, 17, 3, 20, 16, 47, 23, 19, 16, 24, 9, 8, 40, 15, 48, 27, 61, 69, 1, 15, 12, 6, 19, 6, 10, 9, 11, 57, 17, 24, 38, 18, 11, 17, 51, 66, 34, 7, 18, 18, 20, 18, 45, 18, 40, 19, 20, 13, 78, 13, 17, 15, 27, 52, 5, 7, 36, 57, 14, 7, 63, 64, 66, 30, 64, 15, 17, 66, 19, 10, 5, 6, 58, 53, 22, 16, 14, 43, 48, 12, 19, 17, 16, 28, 7, 28, 57, 37, 48, 48, 45, 12, 10, 4, 48, 49, 88, 66, 14, 47, 38, 6, 11, 13, 5, 15, 6, 15, 67, 17, 56, 20, 25, 18, 19, 5, 41, 10, 9, 21, 8, 44, 54, 10, 81, 10, 64, 28, 6, 63, 19, 14, 3, 70, 8, 4, 48, 55, 4, 11, 2, 65, 5, 50, 2, 56, 5, 12, 64, 7, 52, 4, 74, 59, 72, 38, 5, 6, 58, 5, 11, 28, 58, 59, 6, 12, 39, 27, 7, 63, 54, 40, 74, 5, 54, 8, 54, 57, 1, 51, 33, 3, 6, 2, 9, 4, 42, 5, 0, 5, 1, 60, 37, 9, 66, 4, 58, 3, 73, 4, 42, 53, 76, 63, 65, 50, 46, 14, 7, 64, 74, 37, 53, 69, 73, 6, 47, 59, 56, 37, 32, 49, 44, 61, 35, 60, 42, 21, 85, 32, 17, 12, 5, 22, 10, 6, 23, 19, 2, 43, 14, 50, 54, 57, 5, 4, 64, 5, 7, 47, 3, 30, 6, 27, 49, 7, 10, 27, 9, 5, 70, 49, 29, 54, 37, 48, 90, 53, 47, 4, 7, 65, 56, 62, 49, 49, 10, 2, 59, 31, 8, 37, 58, 3, 71, 49, 54, 3, 2, 63, 3, 57, 2, 2, 40, 3, 44, 2, 70, 2, 2, 24, 8, 2, 2, 4, 23, 82, 7, 9, 14, 62, 2, 8, 50, 4, 74, 37, 18, 55, 47, 2, 10, 7, 84, 3, 3, 58, 66, 78, 71, 1, 8, 64, 58, 59, 66, 5, 59, 2, 74, 4, 59, 55, 3, 2, 70, 57, 80, 3, 6, 2, 3, 52, 18, 3, 1, 7, 42, 5, 66, 67, 8, 5, 56, 3, 63, 54, 48, 36, 48, 5, 54, 51, 59, 67, 59, 3, 57, 0, 2, 60, 2, 1, 76, 0, 2, 45, 56, 49, 42, 9, 2, 3, 3, 48, 51, 60, 66, 47, 51, 51, 3, 49, 43, 50, 67, 3, 49, 3, 3, 63, 65, 51, 7, 49, 13, 70, 38, 52, 52, 55, 8, 61, 63, 51, 53, 42, 1, 2, 8, 4, 3, 9, 8, 49, 71, 8, 4, 2, 5, 2, 60, 2, 39, 54, 2, 63, 32, 38, 57, 9, 2, 7, 60, 48, 49, 57, 8, 41, 6, 53, 45, 7, 55, 57, 2, 51, 63, 48, 55, 54, 7, 46, 2, 64, 2, 47, 40, 1, 2, 49, 45, 3, 2, 49, 6, 6, 57, 2, 6, 7, 1, 8, 3, 8, 64, 3, 7, 59, 7, 60, 9, 3, 59, 55, 61, 1, 69, 55, 6, 70, 51, 7, 56, 61, 61, 3, 1, 5, 50, 4, 7, 6, 44, 39, 5, 49, 10, 5, 41, 4, 0, 60, 43, 6, 0, 45, 56, 3, 8, 34, 2, 55, 3, 66, 6, 5, 30, 51, 57, 68, 76, 1, 61, 0, 4, 38, 45, 0, 2, 5, 47, 3, 1, 1, 5, 5, 2, 0, 3, 40, 55, 36, 58, 3, 6, 66, 0, 69, 0, 2, 1, 51, 52, 2, 48, 2, 2, 2, 43, 2, 2, 4, 47, 2, 55, 50, 62, 51, 65, 47, 3, 59, 63, 50, 64, 0, 74, 1, 54, 47, 50, 2, 2, 60, 3, 44, 7, 3, 3, 57, 3, 49, 1, 6, 54, 57, 50, 50, 2, 1, 2, 47, 50, 1, 50, 6, 43, 51, 56, 3, 56, 3, 38, 48, 1, 32, 58, 6, 1, 2, 34, 53, 2, 2, 1, 49, 1, 48, 35, 2, 54, 3, 36, 5, 7, 0, 48, 39, 47, 2, 45, 6, 3, 1, 3, 3, 2, 57, 3, 1, 3, 3, 3, 49, 52, 1, 3, 4, 3, 52, 55, 54, 45, 1, 0, 3, 49, 1, 0, 3, 5, 44, 5, 45, 3, 3, 43, 67, 61, 48, 67, 1, 0, 1, 0, 58, 42, 3, 10, 6, 3, 39, 39, 9, 50, 51, 8, 10, 4, 9, 2, 65, 58, 38, 1, 1, 49, 57, 42, 52, 52, 49, 3, 42, 40, 50, 40, 68, 2, 51, 49, 53, 69, 54, 58, 48, 58, 44, 41, 44, 42, 39, 54, 47, 46, 37, 2, 57, 57, 48, 56, 55, 51, 48, 44, 42, 52, 1, 53, 60, 58, 46, 55, 62, 40, 0, 53, 50, 47, 48, 49, 51, 47, 48, 53, 60, 48, 46, 52, 51, 49, 1, 40, 39, 38, 1, 48, 29, 42, 66, 49, 50, 42, 2, 50, 52, 3, 2, 43, 50, 46, 41, 53, 49, 62, 56, 63, 46, 44, 45, 42, 4, 2, 3, 43, 42, 45, 53, 41, 47, 46, 53, 53, 67, 71, 58, 44, 43, 53, 56, 53, 46, 48, 34, 42, 49, 38, 3, 1, 57, 32, 43, 35, 46, 46, 46, 34, 28, 1, 0, 1, 54, 1, 3, 6, 1, 5, 53, 2, 4, 45, 1, 48, 56, 58, 54, 45, 57, 46, 48, 55, 0, 59, 4, 52, 4, 56, 6, 51, 4, 1, 60, 4, 7, 58, 1, 53, 1, 1, 4, 4, 53, 4, 55, 1, 4, 4, 54, 3, 5, 55, 1, 5, 50, 5, 8, 57, 1, 55, 52, 58]\n",
    "\n",
    "a = np.array(a) \n",
    "b = np.array(b)\n",
    "c = np.array(c)\n",
    "d = np.array(d)\n",
    "e = b + d\n",
    "f = e / (c + e)\n",
    "\n",
    "print(np.sum(f - 0.5) / len(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "d2f9afc3-191a-426a-aef2-ca342606c5d0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(c, 'r-+')\n",
    "plt.legend('implicit')\n",
    "plt.plot(e, 'y-o')\n",
    "plt.legend('explicit')\n",
    "# plt.savefig(\"3.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "2bcc5909-feba-4f8d-9008-cb4714506268",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.2798790551489746\n"
     ]
    }
   ],
   "source": [
    "plt.plot(f)\n",
    "plt.show()\n",
    "print(np.sum(f - 0.5) / len(f))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "825d8bc1-9a57-40cc-b2de-912aa5d4a6b7",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tfdf",
   "language": "python",
   "name": "tfdf"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
